Put the sugar and 1 cup of water in a small pot and bring just to a simmer, stirring occasionally to dissolve the sugar. Remove from the heat, stir in the dried lavender, cover and let steep for at least 20 minutes.
Pour the lavender syrup through a fine-mesh strainer. The syrup can be made up to 3 days in advance and kept cold in the refrigerator.
In a large pitcher, add the lemon juice, lavender syrup, 2 cups of water and ice and stir to combine. Taste, adding more water to reach the desired sweetness.
Pour the lavender lemonade into individual glasses with ice, top with chilled cava and garnish with lemon slices. Enjoy!